Finite Group Databasebeta

← #34004896

Subgroups — #34004896

Order 18688.

516 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625864C211yesmaximal, characteristic
2#22625864C211yesmaximal, characteristic
3C2×#17989446C212yesmaximal
4#22624809C212yesmaximal
5C4×#14556590C211yesmaximal, characteristic
6C2×#14556658—21no—
7C2×#14556658—21no—
8C2×#14556658C2212yes—
9C2×#14556658C2212yes—
10C2×C4⋊#10596833—21no—
11C2×C4⋊#10596833—21no—
12#17989446—24no—
13C2×#14556590C2211yescharacteristic
14C2×C4×Dic146—21no—
15#17988491—21no—
16#17988486C411yescharacteristic
17#17988484—21no—
18#17988483C411yescharacteristic
19#17988456C2211yescharacteristic
20C4×#11924007—21no—
21C4×C4⋊Dic73C411yescharacteristic
22C42×Dic73C2211yescharacteristic
23C4×C4⋊C4×C73C411yescharacteristic
24C22×#10596833—22no—
25C22×#10596833—22no—
26#14556658—22no—
27#14556658—22no—
28#14556658—22no—
29#14556658—22no—
30#14556658—42no—
31#14556658—42no—
32C4⋊#10596833—42no—
33C4⋊#10596833—42no—
34C22×Dic146—21no—
35#14556590—21no—
36#14556590—21no—
37#14556590D412yes—
38#14556590Q812yes—
39C4×Dic146—42no—
40C4×Dic146—42no—
41C2×C4⋊Dic73—21no—
42C2×C4⋊Dic73C2×C411yescharacteristic
43C2×C4⋊Dic73C2×C411yescharacteristic
44C2×#11924007—21no—
45C2×#11924007—21no—
46C2×#11924007—21no—
47C2×#11924007—21no—
48C2×C4×Dic73—21no—
49C2×C4×Dic73C2×C411yescharacteristic
50C2×C4×Dic73D411yescharacteristic
51C2×C4×Dic73D411yescharacteristic
52C2×C4×Dic73D411yescharacteristic
53C2×C4×Dic73D411yescharacteristic
54C2×C4×Dic73C2311yescharacteristic
55#14556498—21no—
56#14556498—21no—
57#14556498—21no—
58C2×C4⋊C4×C73C2×C411yescharacteristic
59C2×C4⋊C4×C73C2×C411yescharacteristic
60C2×C42×C73—21no—
61C2×C42×C73C2×C411yescharacteristic
62#95×C73—21no—
63C2×#10596833—42no—
64C2×#10596833—42no—
65C2×#10596833—42no—
66C2×#10596833—42no—
67C2×#10596833—42no—
68C2×#10596833—42no—
69C2×Dic146—22no—
70C2×Dic146—22no—
71C2×Dic146—41no—
72C2×Dic146—41no—
73C2×Dic146—41no—
74C2×Dic146—41no—
75C22×Dic73—21no—
76C22×Dic73—21no—
77C22×Dic73C22⋊C411yescharacteristic
78C22×Dic73C22⋊C411yescharacteristic
79C22×Dic73C2×D411yescharacteristic
80C22×Dic73C2×D411yescharacteristic
81C4⋊Dic73—21no—
82C4⋊Dic73—42no—
83C4⋊Dic73—41no—
84C4⋊Dic73C4⋊C412yes—
85#11924007—22no—
86#11924007—22no—
87#11924007—42no—
88#11924007—41no—
89#11924007—41no—
90#11924007—41no—
91#11924007—41no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73—41no—
97C4×Dic73—42no—
98C4×Dic73D812yes—
99C4×Dic73SD1612yes—
100C4×Dic73SD1612yes—
101C4×Dic73Q1612yes—
102C4×Dic73C2×D411yescharacteristic
103C4×Dic73C2×Q811yescharacteristic
104C4×Dic73#4111yescharacteristic
105C4×Dic73#4111yescharacteristic
106C22×C4×C73—21no—
107C22×C4×C73—21no—
108C22×C4×C73C22⋊C411yescharacteristic
109C22×C4×C73C22⋊C411yescharacteristic
110C22×C4×C73C22×C411yescharacteristic
111C4⋊C4×C73—21no—
112C4⋊C4×C73—41no—
113C4⋊C4×C73C4⋊C412yes—
114C42×C73—22no—
115C42×C73—42no—
116C23×C73C2×C22⋊C411yescharacteristic
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—22no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73#10112yes—
129C2×C4×C73#10212yes—
130C2×C4×C73#10312yes—
131C2×C4×C73C2×C4⋊C411yescharacteristic
132C2×C4×C73#11711yescharacteristic
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—22no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73#10212yes—
144C2×Dic73#10312yes—
145C2×Dic73#12111yescharacteristic
146C2×Dic73#12111yescharacteristic
147C2×Dic73C22⋊Q811yescharacteristic
148C2×Dic73C22⋊Q811yescharacteristic
149C2×Dic73C2×D811yescharacteristic
150C2×Dic73C2×SD1611yescharacteristic
151C2×Dic73C2×SD1611yescharacteristic
152C2×Dic73C2×Q1611yescharacteristic
153C2×Dic73AGL(1,ℤ/8)11yescharacteristic
154C2×Dic73AGL(1,ℤ/8)11yescharacteristic
155C2×Dic73#13711yescharacteristic
156C2×Dic73#13711yescharacteristic
157Dic146—42no—
158Dic146—42no—
159Dic146—42no—
160Dic146—42no—
161#10596833—82no—
162#10596833—82no—
163C22×C73#38011yescharacteristic
164C22×C73C2×#10111yescharacteristic
165C22×C73#41311yescharacteristic
166C22×C73C2×#10211yescharacteristic
167C22×C73C2×#10311yescharacteristic
168C22×C73#41711yescharacteristic
169C22×C73#41711yescharacteristic
170C4×C73—21no—
171C4×C73—21no—
172C4×C73—42no—
173C4×C73—41no—
174C4×C73—81no—
175C4×C73#33214yescomplemented
176Dic73—22no—
177Dic73—22no—
178Dic73—42no—
179Dic73—81no—
180Dic73#45911yescharacteristic
181Dic73#46011yescharacteristic
182Dic73#46111yescharacteristic
183Dic73#46211yescharacteristic
184Dic73#47411yescharacteristic
185Dic73#47511yescharacteristic
186Dic73#47611yescharacteristic
187Dic73#47711yescharacteristic
188#8586—731nomaximal, Sylow
189C2×C73C2×#33211yescharacteristic
190C2×C73#154711yescharacteristic
191C2×C73#155011yescharacteristic
192C2×C73#156111yescharacteristic
193C2×C73#180111yescharacteristic
194C2×C73#180211yescharacteristic
195C2×C73#180311yescharacteristic
196C4×C4⋊Q8—731no—
197#1842—731no—
198#1842—731no—
199C2×#332—732no—
200#1296—732no—
201C73#858611yescharacteristic, complemented, Sylow
202C2×C4⋊Q8—731no—
203C2×C4×Q8—1461no—
204C2×C4⋊C8—732no—
205C2×C4⋊C8—732no—
206C2×C4⋊C8—1461no—
207C2×C4⋊C8—1461no—
208C2×C4⋊C8—1461no—
209C2×C4⋊C8—1461no—
210#391—1461no—
211#389—731no—
212#389—731no—
213#389—1461no—
214#384—731no—
215C4×C4⋊C4—731no—
216C4×C4⋊C4—1461no—
217C4×C4⋊C4#6440811yescharacteristic
218C43—731no—
219#332—1464no—
220C22×Q8—1461no—
221C22×C8—1462no—
222C22×C8—1462no—
223C4⋊Q8—732no—
224C4⋊Q8—732no—
225C4⋊Q8—1461no—
226C4⋊Q8—1461no—
227C4×Q8—2922no—
228C4×Q8—2922no—
229C2×C4⋊C4—731no—
230C2×C4⋊C4—731no—
231C2×C4⋊C4—1461no—
232C2×C4⋊C4—1461no—
233C2×C4⋊C4—1461no—
234C2×C4⋊C4—1461no—
235C2×C4⋊C4—1461no—
236C2×C4⋊C4C2×#6440811yescharacteristic
237C2×C4⋊C4C2×#6440811yescharacteristic
238C2×C42—21no—
239C2×C42—731no—
240C2×C42—731no—
241C2×C42—731no—
242C2×C42—731no—
243C2×C42—731no—
244C2×C42—731no—
245C2×C42—1461no—
246C2×C42C2×#6440811yescharacteristic
247C4⋊C8—2922no—
248C4⋊C8—2922no—
249C4⋊C8—2922no—
250C4⋊C8—2922no—
251C4⋊C8—1462no—
252C4⋊C8—1462no—
253C4⋊C8—1462no—
254C4⋊C8—1462no—
255#95—21no—
256#95—1461no—
257#95—1461no—
258#95—1461no—
259C2×Q8—2921no—
260C2×Q8—2921no—
261C2×Q8—2921no—
262C2×Q8—2921no—
263C2×Q8—1462no—
264C2×Q8—1462no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—731no—
268C22×C4—731no—
269C22×C4—731no—
270C22×C4—731no—
271C22×C4—1461no—
272C22×C4—1461no—
273C22×C4C22⋊#6440811yescharacteristic
274C22×C4C22⋊#6440811yescharacteristic
275C22×C4C22×#6440811yescharacteristic
276C2×C8—2922no—
277C2×C8—2922no—
278C2×C8—2922no—
279C2×C8—2922no—
280C2×C8—2922no—
281C2×C8—2922no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—2921no—
285C4⋊C4—2921no—
286C4⋊C4—2921no—
287C4⋊C4—2922no—
288C4⋊C4—2921no—
289C4⋊C4—2921no—
290C4⋊C4—2922no—
291C4⋊C4—732no—
292C4⋊C4—1462no—
293C4⋊C4—1462no—
294C4⋊C4—1461no—
295C4⋊C4C4⋊#6440812yes—
296C42—22no—
297C42—42no—
298C42—2921no—
299C42—2922no—
300C42—732no—
301C42—732no—
302C42—732no—
303C42—732no—
304C42—731no—
305C42—731no—
306C42—731no—
307C42—731no—
308C42—1461no—
309C42—1461no—
310C42—1461no—
311C42—1461no—
312C23C2×C22⋊#6440811yescharacteristic
313Q8—2922no—
314Q8—2922no—
315Q8—2922no—
316Q8—2922no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—2921no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—2921no—
332C2×C4—2921no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—731no—
336C2×C4—731no—
337C2×C4—731no—
338C2×C4—731no—
339C2×C4—731no—
340C2×C4—731no—
341C2×C4—731no—
342C2×C4—731no—
343C2×C4—731no—
344C2×C4—731no—
345C2×C4—732no—
346C2×C4—732no—
347C2×C4—1462no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4#1455665212yes—
353C2×C4#1455665312yes—
354C2×C4#1455665412yes—
355C2×C4C2×C4⋊#6440811yescharacteristic
356C2×C4#1455667011yescharacteristic
357C8—5842no—
358C8—5842no—
359C22#1798952911yescharacteristic
360C22C2×#1455665211yescharacteristic
361C22#1798957311yescharacteristic
362C22C2×#1455665311yescharacteristic
363C22C2×#1455665411yescharacteristic
364C22#1798957811yescharacteristic
365C22#1798957811yescharacteristic
366C4—21no—
367C4—21no—
368C4—42no—
369C4—41no—
370C4—81no—
371C4—2922no—
372C4—5841no—
373C4—731no—
374C4—731no—
375C4—731no—
376C4—731no—
377C4—731no—
378C4—731no—
379C4—731no—
380C4—731no—
381C4—1462no—
382C4—1462no—
383C4#1798944614yescomplemented
384C2C2×#1798944611yescharacteristic
385C2#2262544211yescharacteristic
386C2#2262544811yescharacteristic
387C2#2262547011yescharacteristic
388C2#2262579711yescharacteristic
389C2#2262579911yescharacteristic
390C2#2262580011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC4×C4⋊C4×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC4×C4⋊C4#64408
hypocenterC73#8586
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
175. C4×C73#332semidirect
201. C73#8586semidirect
383. C4#17989446semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226258642
C2×#179894462
#226248092
C4×#145565902
#858673